As civilization fell into ruin, some were better defended than others. In the deserts, safely isolated governors were able to establish control of the population. On the coasts, a few established city states were able to take advantage of trade routes, and buy themselves out of any trouble. However, in much of the interior of the country, people were lost, confused, and very willing to fight among themselves. Not to mention the constant threats from Barbarians that stalked the frontiers. Only the strong had a chance in this world, and the weak clung to them.
Feudal States were forged out of these fires. Peasants till the fields for the Warlords, who in turn, protect the--even if that often means protection from them. The wide open spaces of the Midwest and Deep South, with fertile fields and longer growing seasons (If not both) were easily able to establish agrarian communities. Much of these kingdoms are therefore located in the Feudal Core, the Heartland of America. However, just outside the core are other very fertile territories like New York and New Jersey, which are smaller but still operate under the same agrarian fiefdom system. The distance between communities in America's interior also plays a big part. Warlords pretty much have carte blanche to run things as they see fit, and the only way to get rid of one if for another warlord to take him out and conquer his territory.
This is where the nature of Feudalism really comes into play. Maintaining swaths of land can be a full time job, so we begin to see delegation. Once a nation or lineage is established, the head of state will allot various counties to allies and vassals, who, depending on the size of the territory, further divide up land among his vassals. These men are generally allowed to do as they wish, just as long as they swear loyalty above. Most Warlords usually possess estates surrounded by villages, as well as a church. Pyramid mounds of earth are built to place the castle on top of. On the frontiers of civilization, especially large fortresses like Rock Island and Macon exist.
This system pretty much allows for little central government, as allies can become enemies, vassals can become usurpers, and devastating wars can be declared at the drop of a hat. As a result, the many different cultures of the feudal zone is constantly in flux. Borders change constantly, and dialects evolve into different languages. The only thing keeping the Feudal Core cohesive in any way is the American Non-Denominational Church. Much of the continuity of the East is found in the Church's documentation, interpretation, and communication between districts.
Though the relationship isn't always perfect, (On account of the Warlords' habit of slaughtering each other and making attempts at unity hard) the Kingdoms and the Church can often have a symbiotic relationship. The Church provides the warlords with bridges, hospitals, and the rather tedious things in life they can't or don't want to bother with. And in turn, the Warlords serve as protectors of the faith on the frontiers. The worry is constantly on the Barbarians that surround the Heartland, and as a result, we've seen the cultures bleed a little into each other. Thus, we see somewhat similar Feudal structures for Voodoo Louisiana, New Israelite Texas, and Catholic Quebec.
As America was built on a rejection of monarchies, feudal lords tend not to have European titles like "King" and "Duke", but "President" "Colonel" and "Governor". It was with these distinctions of American nobility, feudal lords were pretty much able to get away with acting like medieval rulers from pretty much any other country.